Finite Group Databasebeta

← #10604643

Subgroups — #10604643

Order 640.

230 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#66058C211yesmaximal, characteristic
2D5⋊#101C212yesmaximal, complemented
3#64929C212yesmaximal, complemented
4#64856C212yesmaximal, complemented
5C2×#713C411yescharacteristic
6C2×Q8×D5C2211yescharacteristic
7D5⋊M16—22no—
8C5×C4⋊Q8C411yescharacteristic
9#4093C411yescharacteristic
10#4090C2211yescharacteristic
11#4042—22no—
12#4040—22no—
13#4021C2211yescharacteristic
14#4018C411yescharacteristic
15#4005—22no—
16#4005C2214yes—
17#2133—51nomaximal, Sylow
18C2×C5×Q8C2×C411yescharacteristic
19C2×C5×Q8C2×C411yescharacteristic
20#713—42no—
21Q8×D5—42no—
22C2×D20—21no—
23C2×D20C2×C411yescharacteristic
24C2×C4×D5—21no—
25C2×C4×D5C2×C411yescharacteristic
26C2×C4×D5D412yes—
27C2×Dic10D412yes—
28C2×Dic10C2311yescharacteristic
29#704—24no—
30#700—42no—
31D5⋊C8—42no—
32C5×C4⋊C4—22no—
33C42×C5C2×C411yescharacteristic
34#685—21no—
35#685—22no—
36#685—22no—
37#683—21no—
38#683—22no—
39C4×Dic5C2×C411yescharacteristic
40#536—51no—
41C2×#101—52no—
42#356—52no—
43#355—52no—
44C22×D5—21no—
45C22×D5C22⋊C411yescharacteristic
46C5×Q8—41no—
47C5×Q8—41no—
48C2×C4×C5—21no—
49C2×C4×C5—21no—
50C2×C4×C5C22⋊C412yes—
51C2×C4×C5C22×C411yescharacteristic
52C2×Dic5—21no—
53C2×Dic5C22⋊C411yescharacteristic
54C2×Dic5C2×D412yes—
55D20—41no—
56D20—42no—
57C4×D5—22no—
58C4×D5—22no—
59C4×D5—22no—
60C4×D5—42no—
61Dic10—42no—
62Dic10—41no—
63#170—44no—
64C2×#41—51no—
65C22×Q8—51no—
66C2×M16—102no—
67C4⋊Q8—51no—
68C4⋊Q8AGL(1,𝔽5)11yescharacteristic
69#124—51no—
70#124—51no—
71#123—102no—
72C22⋊Q8—102no—
73#117—51no—
74#101—54no—
75#101—102no—
76C22×C5C2×C22⋊C411yescharacteristic
77C2×D5—41no—
78C2×D5—42no—
79C2×D5—41no—
80C2×D5#9912yes—
81C4×C5—21no—
82C4×C5—22no—
83C4×C5—41no—
84C4×C5—41no—
85Dic5—22no—
86Dic5—21no—
87Dic5—41no—
88#41—202no—
89C2×Q8—52no—
90C2×Q8—51no—
91C2×Q8—202no—
92C2×Q8C2×AGL(1,𝔽5)11yescharacteristic
93C2×Q8C2×AGL(1,𝔽5)11yescharacteristic
94C2×D4—51no—
95C2×D4—101no—
96C22×C4—52no—
97C22×C4—51no—
98C22×C4—101no—
99M16—104no—
100M16—202no—
101C2×C8—202no—
102C4⋊C4—22no—
103C4⋊C4—101no—
104C4⋊C4—102no—
105C22⋊C4—102no—
106C22⋊C4—101no—
107C22⋊C4—102no—
108C42—51no—
109C42C2×AGL(1,𝔽5)11yescharacteristic
110C2×C5—21no—
111C2×C5C2×#9911yescharacteristic
112D5—22no—
113D5—81no—
114C23—51no—
115C23—101no—
116Q8—41no—
117Q8—41no—
118Q8—202no—
119Q8—201no—
120D4—201no—
121D4—202no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—52no—
125C2×C4—51no—
126C2×C4—102no—
127C2×C4—102no—
128C2×C4—102no—
129C2×C4—101no—
130C2×C4—202no—
131C2×C4C22⋊AGL(1,𝔽5)12yes—
132C2×C4C22×AGL(1,𝔽5)11yescharacteristic
133C8—204no—
134C5#213311yescharacteristic, complemented, Sylow
135C22—52no—
136C22—201no—
137C22—202no—
138C22—201no—
139C22C2×C22⋊AGL(1,𝔽5)11yescharacteristic
140C4—22no—
141C4—21no—
142C4—41no—
143C4—41no—
144C4—102no—
145C4—101no—
146C4—201no—
147C2—21no—
148C2—102no—
149C2—401no—
150C2D5⋊#9911yescharacteristic
subgroupG/H
centerC2D5⋊#99
commutatorC2×C4×C5C22×C4
FrattiniC2×C4C22×AGL(1,𝔽5)
FittingC5×C4⋊Q8C4
socleC2×C5C2×#99
prime radicalC2×#713C4
cosocleC2×Dic10C23
hypercenterC4⋊Q8AGL(1,𝔽5)
hypocenterC5#2133
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. D5⋊#101C2semidirect
3. #64929C2semidirect
4. #64856C2semidirect
134. C5#2133semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#660582
D5⋊#1012
#649292
#648562
#21335